{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Process (GP) smoothing\n",
    "\n",
    "This example deals with the case when we want to **smooth** the observed data points $(x_i, y_i)$ of some 1-dimensional function $y=f(x)$, by finding the new values $(x_i, y'_i)$ such that the new data is more \"smooth\" (see more on the definition of smoothness through allocation of variance in the model description below) when moving along the $x$ axis. \n",
    "\n",
    "It is important to note that we are **not** dealing with the problem of interpolating the function $y=f(x)$ at the unknown values of $x$. Such problem would be called \"regression\" not \"smoothing\", and will be considered in other examples.\n",
    "\n",
    "If we assume the functional dependency between $x$ and $y$ is **linear** then, by making the independence and normality assumptions about the noise, we can infer a straight line that approximates the dependency between the variables, i.e. perform a linear regression. We can also fit more complex functional dependencies (like quadratic, cubic, etc), if we know the functional form of the dependency in advance.\n",
    "\n",
    "However, the **functional form** of $y=f(x)$ is **not always known in advance**, and it might be hard to choose which one to fit, given the data. For example, you wouldn't necessarily know which function to use, given the following observed data. Assume you haven't seen the formula that generated it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "figsize(12, 6);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "\n",
    "x = np.linspace(0, 50, 100)\n",
    "y = (np.exp(1.0 + np.power(x, 0.5) - np.exp(x/15.0)) + \n",
    "     np.random.normal(scale=1.0, size=x.shape))\n",
    "\n",
    "plot(x, y);\n",
    "xlabel(\"x\");\n",
    "ylabel(\"y\");\n",
    "title(\"Observed Data\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's try a linear regression first\n",
    "\n",
    "As humans, we see that there is a non-linear dependency with some noise, and we would like to capture that dependency. If we perform a linear regression, we see that the \"smoothed\" data is less than satisfactory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, y);\n",
    "xlabel(\"x\");\n",
    "ylabel(\"y\");\n",
    "\n",
    "lin = stats.linregress(x, y)\n",
    "plot(x, lin.intercept + lin.slope * x);\n",
    "title(\"Linear Smoothing\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Linear regression model recap\n",
    "\n",
    "The linear regression assumes there is a linear dependency between the input $x$ and output $y$, sprinkled with some noise around it so that for each observed data point we have:\n",
    "\n",
    "$$ y_i = a + b\\, x_i + \\epsilon_i $$\n",
    "\n",
    "where the observation errors at each data point satisfy:\n",
    "\n",
    "$$ \\epsilon_i \\sim N(0, \\sigma^2) $$\n",
    "\n",
    "with the same $\\sigma$, and the errors are independent:\n",
    "\n",
    "$$ cov(\\epsilon_i, \\epsilon_j) = 0 \\: \\text{ for } i \\neq j $$\n",
    "\n",
    "The parameters of this model are $a$, $b$, and $\\sigma$. It turns out that, under these assumptions, the maximum likelihood estimates of $a$ and $b$ don't depend on $\\sigma$. Then $\\sigma$ can be estimated separately, after finding the most likely values for $a$ and $b$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Process smoothing model\n",
    "\n",
    "This model allows departure from the linear dependency by assuming that the dependency between $x$ and $y$ is a Brownian motion over the domain of $x$. This doesn't go as far as assuming a particular functional dependency between the variables. Instead, by **controlling the standard deviation of the unobserved Brownian motion** we can achieve different levels of smoothness of the recovered functional dependency at the original data points. \n",
    "\n",
    "The particular model we are going to discuss assumes that the observed data points are **evenly spaced** across the domain of $x$, and therefore can be indexed by $i=1,\\dots,N$ without the loss of generality. The model is described as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "z_i & \\sim \\mathcal{N}(z_{i-1} + \\mu, (1 - \\alpha)\\cdot\\sigma^2) \\: \\text{ for } i=2,\\dots,N \\\\\n",
    "z_1 & \\sim ImproperFlat(-\\infty,\\infty) \\\\\n",
    "y_i & \\sim \\mathcal{N}(z_i, \\alpha\\cdot\\sigma^2)\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "where $z$ is the hidden Brownian motion, $y$ is the observed data, and the total variance $\\sigma^2$ of each ovservation is split between the hidden Brownian motion and the noise in proportions of $1 - \\alpha$ and $\\alpha$ respectively, with parameter $0 < \\alpha < 1$ specifying the degree of smoothing.\n",
    "\n",
    "When we estimate the maximum likelihood values of the hidden process $z_i$ at each of the data points, $i=1,\\dots,N$, these values provide an approximation of the functional dependency $y=f(x)$ as $\\mathrm{E}\\,[f(x_i)] = z_i$ at the original data points $x_i$ only. Therefore, again, the method is called smoothing and not regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's describe the above GP-smoothing model in PyMC3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "from theano import shared\n",
    "from pymc3.distributions.timeseries import GaussianRandomWalk\n",
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a model with a shared parameter for specifying different levels of smoothing. We use very wide priors for the \"mu\" and \"tau\" parameters of the hidden Brownian motion, which you can adjust according to your application."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '16678' (I am process '16664')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /.theano/compiledir_Linux-4.15--generic-x86_64-with-debian-buster-sid-x86_64-3.6.8-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '16678' (I am process '16664')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /.theano/compiledir_Linux-4.15--generic-x86_64-with-debian-buster-sid-x86_64-3.6.8-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '16678' (I am process '16664')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /.theano/compiledir_Linux-4.15--generic-x86_64-with-debian-buster-sid-x86_64-3.6.8-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '16678' (I am process '16664')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /.theano/compiledir_Linux-4.15--generic-x86_64-with-debian-buster-sid-x86_64-3.6.8-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '16678' (I am process '16664')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /.theano/compiledir_Linux-4.15--generic-x86_64-with-debian-buster-sid-x86_64-3.6.8-64/lock_dir\n"
     ]
    }
   ],
   "source": [
    "LARGE_NUMBER = 1e5\n",
    "\n",
    "model = pm.Model()\n",
    "with model:\n",
    "    smoothing_param = shared(0.9)\n",
    "    mu = pm.Normal(\"mu\", sigma=LARGE_NUMBER)\n",
    "    tau = pm.Exponential(\"tau\", 1.0/LARGE_NUMBER)\n",
    "    z = GaussianRandomWalk(\"z\",\n",
    "                           mu=mu,\n",
    "                           tau=tau / (1.0 - smoothing_param), \n",
    "                           shape=y.shape)\n",
    "    obs = pm.Normal(\"obs\", \n",
    "                    mu=z, \n",
    "                    tau=tau / smoothing_param, \n",
    "                    observed=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also make a helper function for inferring the most likely values of $z$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def infer_z(smoothing):\n",
    "    with model:\n",
    "        smoothing_param.set_value(smoothing)\n",
    "        res = pm.find_MAP(vars=[z], fmin=optimize.fmin_l_bfgs_b)\n",
    "        return res['z']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please note that in this example, we are only looking at the MAP estimate of the unobserved variables. We are not really interested in inferring the posterior distributions. Instead, we have a control parameter $\\alpha$ which lets us allocate the variance between the hidden Brownian motion and the noise. Other goals and/or different models may require sampling to obtain the posterior distributions, but for our goal a MAP estimate will suffice.\n",
    "\n",
    "### Exploring different levels of smoothing\n",
    "\n",
    "Let's try to allocate 50% variance to the noise, and see if the result matches our expectations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/repos/pymc3/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "/repos/pymc3/pymc3/tuning/starting.py:102: UserWarning: In future versions, set the optimization algorithm with a string. For example, use `method=\"L-BFGS-B\"` instead of `fmin=sp.optimize.fmin_l_bfgs_b\"`.\n",
      "  warnings.warn('In future versions, set the optimization algorithm with a string. '\n",
      "logp = -4.6549e+06:   0%|          | 16/5000 [00:01<07:29, 11.10it/s]  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoothing = 0.5\n",
    "z_val = infer_z(smoothing)\n",
    "\n",
    "plot(x, y);\n",
    "plot(x, z_val);\n",
    "title(\"Smoothing={}\".format(smoothing));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that the variance is split evenly between the noise and the hidden process, as expected. \n",
    "\n",
    "Let's try gradually increasing the smoothness parameter to see if we can obtain smoother data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/repos/pymc3/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "/repos/pymc3/pymc3/tuning/starting.py:102: UserWarning: In future versions, set the optimization algorithm with a string. For example, use `method=\"L-BFGS-B\"` instead of `fmin=sp.optimize.fmin_l_bfgs_b\"`.\n",
      "  warnings.warn('In future versions, set the optimization algorithm with a string. '\n",
      "logp = -5.2675e+06:   1%|          | 37/5000 [00:00<00:06, 741.11it/s] \n"
     ]
    },
    {
     "data": {
      "image/png": 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x2rIL/n0cLP8nLPw+/M8yOOnXuMtOZkWDgd++vIEGd4A7L5hDmqUjI6VU30W6vrqbiF3//u2NWhTek7BXFDj4PDqdjxbdD55muO84xn1+MwvEZoozLUljNWFvjzfA9oci3PXO1l5LEigUiqFDCXuKiPnriyo0Id3RQ4Rb1eLD5Q9zWKGAJy6A9nq49EU483awaII9bWwGDe4AL62t5doTJzJb35QUozDDisVoiEfsOd1E7O9saiDHbk7Kk0+kLNeO0SBYFZ0EV/wXyo5gcvXzPGu9hbz/LIBtS+NjK/LTcfnD8df4wuoa7npnG29uqNvn90mhUBx4lLD3kzZvqNeKiLFiXAt1Yd/Wgx2zvqYNIxFO3/QLLWK/6HE45MSkMdPGaouqs0uzueaEiV2uYTAISnLSaNBrymSnJXvsoD1o5pfnJnVSSsRsNFCWa9fqwIw5FC56nBsOeZFbrNcjLBnw+Dfg1esg4GZCQfIC6tMrqwDYUte75aRQKIYGlRXTTy5f8gVr9rQyJtPG7NIsLlk0nmMT0gJbPJotMbs0G4vJwPYeFlA/3dHE762PklHzMZxzL5Qf3WXMvPE5fPvwMr53zATNh++GcTlp7GryYBCQYev4M+Ym2DILe7BhYlTkJ3vnu1wCR8Fp8J0b4P0/wKd/g50fMPnc5wGtvk2GzcS6qlYAtvSxlqBQKIYGFbH3kwZXgBnFmRw+IZfPdjRz97vbks7HIvY8h4VDCtK7zYyRUpK78VEuFm/DkdfCYZd2ey+b2cjvzz2U8Xnd2yjQUa0xK82MwdARladZjNjM2p+124yYBCryHVQ2e4hGNe+8ttVHcbYNzDY49Va44nXwNFP85pVkmMLsbPTw9IoqzEbBydMKe60dr1Aohg4l7P3EGwxzWFkOd100l5OnFXWxZVo8QewWIzazkUmF6Wxr6Cp6e9e/z4+DD1Cdfwyc/LsBzSeW8pi4cBoj127BZjYklQTujgkFDvyhKHUuP8FwlAZ3IDkjZvyRcP79iL3ruCvtP2za6+LFNTWcOn0Mh0/Io6k9QFN7zz1aFQrF0JASYRdC/EQI8ZUQYoMQ4kkhhK3v3xpeeIMR7HpmSlGWjXqXPx7pgpYVExPZSYXpVLX48AYTmkq7asl57SqqZT7R8+4Dw8DqrsQyY7LtXWvSjMmysaA8N16SoCfim48aPdS1+ZGya6ojU86AE2/ipNCHTN21hFZviAsWlMbXAZTPrlAcfAxY2IUQJcCPgflSypmAEbhooNc9mIhGJYFwNF4Ea2yWjXBU0pxQHtfpDcYzUiYVadvwdzTo/nU4AM9chgh5uNnxK8qKiwc8p1gue3Y3Efs9F8/lL9+c3ec1JuTr5QKa2hM2J6V1HXjM9WzOPYn/Mz7J+elfcfTEfKaM0TZXbVbCrlAcdKTKijEBaUIIE2AHalN03YMCXygC0BGxZ3btQNTiDcUzUiYWaqK3rcEN0Qi89EOoXsEN4R9SNmVeSuYUa3XXXcQ+LsdOYWbfH5qKMq2kmY3sbPL0uDkJACHYuPBPbJTj+aO8C2PjRvLTreSnW9ncTVMQhUIxtAxY2KWUNcAdwB5gL9AmpXx7oNc9mOgs7LFGFYllb52eILm6yI7Ps2M2Ci3l8bWfwIbn2D33Bl4JzU/KpBkIeQ4LeQ5L9xF2PxFCUJHvYFeCsI/N6v6BcMS0Mh4Y9ydMtgx44kJw1zN1TIbKjFEoDkJSYcXkAIuBCqAYcAghvt3NuKuFECuFECsbGxsHettBxRfUhD3RioGuwh6L2M1GAxV5dmZv/iusfhiOuZ4nLOdhMgiOOCQvJXMSQvDKtUfzg+MPGdB1YuUCYg02eqq5PjYrjbuvPhPjJU+Dtxme+hYzC81sqXMTSVhrUCgUQ08qrJiTgV1SykYpZQh4ATiy8yAp5X1SyvlSyvkFBamJWgcLbzAWsWv54nnpVowGQV2bFuUGw1HcgXBSDvm1ppc4ve0ZQvOughN/zUdbm5g3Pod0a+q2DpRkp8XntL9MyHdQ7fSyq8nTv+i/eA6cdx/UrOTc1kcIhKNUNqs6MgrFwUQqhH0PcLgQwi60bY4nAZtScN2Dhs5WjNEgKMywUtempfq16jnssYidz/7O2S0P8XzkGI758jSWfFrJpr2ulNkwqaSiwEFUwuo9rd37690x7Ww47DKm7HqYmWKnyoxRKA4yUuGxLweeA1YD6/Vr3jfQ6x5MxNIWE22KokxbvHF1rHNSrsMCKx+Ct26E6YupuPIhCrPs3PzqRoCkBhYHCxV6ZkwwHO2/sAOccis4CrndfD9ba1oO0OwUCsX+kJKsGCnlb6WUU6WUM6WUl0opR9SuFV8wOWIHzWffq1sxseJYhzS+oy2WTjoVznuAw8oLeOmHR3H7N2Zx1dEVTB978HUgiuWyQw8ZMT2Rlo046w6mG3ZTtuU/AFS1eDntzo/46dNrVQNshWIIUbVi+kHMikksnVuUaePjbU2A1nnIjp9DVvwOiufCBY+A3qrOYBBcML+060UPErLSzOSnW2hqDyY12OgX085mTfqxnOV8hPaaq7jymUZqW/3sbvHw0toaFs8p4ddfmx7P71coFIODKinQD2KLp2kJVsyYLBvtgTBuf4gWT5DvGf+LydcIZ9wO5v1PQRwKYlH7PkXsOqtn3IhPWti75LvsbnTx70vn8fENJ3Ll0RW8vLaGBz/ZlerpKhSKPlDC3g/8oe6tGIB6lx+/cy9Xm14jOm0xlC4YkjkOhIEIe2lZBb8JXcGk0CaePnQFR03MpyDDyq/Omk5hhi0pJVShUAwOStj7QTxi72TFANS1BZi9819YCGM4+bdDMr+BctK0Io6emE/eflgms8Zl8zpHsin3JOZs+wfUbYify3VY4usPCoVi8FDC3g9iwm4zJVgxurC3127isMaXecV8GuQNbLPQUHHajDE8dtWiHpty9MaYLBvLbzyZqVfeB2k58OL/QFgvYZxuSaqno1AoBgcl7P3AH4qQZjYm1T0fk2VDEGXa2j8QFDZezuqy2XbUkJduRTjy4Zx7oH49fHInEIvYR1SClEIxLFBZMf3AGwwn2TCg5bT/IO0dxjs/45+OH2BMP/hy1AedKWfAjPPgk7/C7As1YW/vGrE/sXwPm/a6mDUui9ml2UwsSE96aCoUioGhhL0f+ILRpIwYAPZ+yf/Kx1hjP5LHwqewSKX0aZz6e9j6Frz1K/IKb8YTjOAPRZI2d/39/e3xMsEAi+cUc/dFc4ditgrFiERZMf3AF+oUsQc98PyVeIxZ/Nl6DU5fKKlOzKgmqwSO+zlsfo2ZvhUASQuoUkoa3QGuPnYCS39yLMdMymf5TrVzVaFIJUrY+0Fi9yQAlv4WmrbxXNmv2eA04w1GOurEKODwayBvIgs23YaFUJKwt3pDBCNRijJtTCrK4IhD8qhz+WnzhYZwwgrFyEIJez/wBSMdVkxbNax6CBZcSXvxUbj8Wh2Z7nqPjlpMFjjjdhztu7nc+GZSZkyDW1tMLcywAjBZb0qyvZsesQqFYv9Qwt4PfKFIhxXz2d+1r0ddl9SUItfRtZPRqGbiSXjLTuD7ptdoa+uwWhrc2oalmLDHWuxtrVe1ZRSKVKGEvR/ErRhvC6xaAod+E7LLKEoQdhWxdyV67P+RJ9wUbXkifqzBpUfs+j6Akuw00sxGtqpOTApFylDC3g98QT2r44v7IOSFo64DOjYpAarQVTc4Djmcj6OzmFn5sLbgTIcVU6BH7AaDYFJROttUxK5QpAwl7P3AF4qQZQzC8n/B5DOgcBqQ3B9ULZ52RQjBEvOFOMJOWPkgAI3uAHaLMamT1KRC1TtVoUglStj7gS8Y4Yi218HnhKN/Ej+elWbGatLewuw05bF3R03GLDamHQbL7oaglwa3P+6vx5hclE6jOxDvRKVQKAaGEvY+iEYlvlCYhQ3PQtkRULYofk4IwZgsG1lpZkxG9VZ2R67DwhO2i8HTCMv/RYM7QGFGct33yUVqAVWhSCVKjfrAH44wTewh218Nsy/qcn5Mpk35672Q67CwLDQZpn4N3v8Dxa2rKMjsFLHHM2OUHaNQpAIl7H3gC0Y43bgCiYApZ3U5f9HCUi5ZVDYEMxse5DksNLcH4Nx/QE4Fv/HexiRL8k7T4iwb6VYT25SwKxQpQQl7H3iDEU41rKAp9zDoptDX1+eO46pjJgzBzIYHuQ4rLn+YkDkD7/mPYiLCJZU3QtAbHyOEYGJhulpAVShShBL2Pgg3bWeaoYqGkpOHeirDktx0zaZyeoLUW8r4cehH5LdvhTduSBo3WaU8KhQpQwl7H1i3vQ5A6/jThngmw5NYV6ZmT5BGd4APonOonnYVrHkUalbFx00uyqDZE9RsG4VCMSBSIuxCiGwhxHNCiM1CiE1CiCNScd2DgYzKt9gQLUfkjB/qqQxLYgvLLZ5gvJyA74ifQnoRvPF/ICUAk1RmjEKRMlIVsd8NvCmlnArMBjal6LpDi7uOjMbVvBlZgN2iStfvD4kRe6ycQH5ePpz0W6heAeufBWCKLuzbVDEwhWLADFjYhRCZwLHAfwCklEEpZetAr3tQsPk1AN6KLujaaEPRL+IRe3uABncAs1GQYzfD7IuheC4s/Q0E2inKtJJhM7GlTgm7QjFQUhGxTwAagYeEEGuEEA8IIRydBwkhrhZCrBRCrGxsbEzBbQeBTa/hdpSzTZYk12NX9JtsuwUhOqyYgnSr1jTbYIAzbgf3Xlh2F0IIJhdlqFx2hSIFpELYTcBhwD+llHMBD/CLzoOklPdJKedLKecXFBxc/UErmzxUNnkIR6IdB/d+CTs/YFfRqYBIau2m6D9GgyDHbokvnhYklhMoXQjTF8Py+yDo4dCSLNbXtBEMR3u+oEKh6JNUCHs1UC2lXK7//Bya0A8L3P4Qp975Ecff8QFTf/0mJ9zxAR9tbYR3fgtp2awqvgRARewDINdh0SJ2V4CCTuUEWPQDCLTB+mdZWJGLPxRlQ23b0ExUoRghDFjYpZR1QJUQYop+6CRg40CvO1jUtfkJRqJcvLCM/znuEGpbfez+4lXY8R4c+3NapR1AeewDINehR+ztAQo7lROg7HAonAFfPMCC8TkAfLFr33uguv0h/rp0a/KnLoVilJKqrJhrgceFEF8Cc4A/pui6B5xGvT74ObOL+dlpUyjJsnJ81d8huwwWXIU/FMFqMmAwiCGe6fAlz2Gh3uWnxRPsUtkRIWDhVVC/noLWtUwocOyXsH+4tZF73t3GhlpXimatUAxfUiLsUsq1un8+S0p5rpTSmYrrDgbxHpx6JLnY+Cmlge1aOp7J2rWRtWKfyXVY2NOilRDoXNkRgEMvAGsmrHiARRW5rKhsIRKV+3QPl0/rPesNhAc8X4ViuDPqd57GNs0UZFghHODb3ofZapgIM84DtCYbKod9YOSlW2P7kLpG7ADWdJjzLfjqJY4ZG8XtD+9z2qPLHwLAE4wMdLoKxbBn1At7ozuAzWwgw2qC1Y+QF27gTi7W0vGItcUb9W/TgMhLKGtc0J2wAyy4CqIhjnK/AcAXu5r36R4unybs3qCK2BWKUa9YDXoKnggH4OO/UJ05lzd9U+OLcN5gWEXsAySxXn2XxdMY+ZNgwvFkffU447KsfFG5bz57PGIPqIhdoRj1wt4Y6+izagm497Jxyo+QUtDi0dq0+UIRlREzQGIRuxCQn96DsAPMvRTaqvhW0R6+2NWClP332d1+3WNXEbtCoYS9wR2gxCHhk79C+TFEyo4CoKldF/ZghDS1eDogYqV7c+0WzL21EJx6FlizODP8Lk3tQXY2efp9j5gVoyJ2hUIJO43uAGcG3oD2ejjhRvJ1D7hJLx+rLZ4qYR8IMSumR389hjkNDj2fsoZ3SMe7T2mPLhWxKxRxRrWw+0MRAr52jm14DCacAOOPjFsFMWH3BpUVM1By7JqwF2Z2k+rYmTmXYAj7udC+at+EPRaxK2FXKEa3sDe1B1hs/BR7yAnHXA9Anm4bNCsrJmWYjQZyHRbG9LRwmkjJPMifzMWWT1i9p//bIWKLp15lxSgUjOp0jwaXn8uNb9GeNYX08qMByLCasJgMSVaMitgHzr3fmsu4bHvfA4WAOd9i4js3Y41U9vv6sQ1KKmJXKEZ5xB6qTT15AAAgAElEQVTetYxphj20zbpCExS0xsr5DgtN7UGklMpjTxFHHpJPWV4/hB1g1oVEMfA1+QG+fmw4CkWi+ELaOK/aoKRQjG5hL9r0MK3SgXnOhUnH8zOsNLUH8IeiSAlpKo99cMkspq7gCM43fozT4+9zeCzVEcCjSgooFKNH2GtafRz/5/fZFmvk0FZNaf17PBM5ntzs7KSx+emasMeiwDS183TQaaz4OiWimcCOT/ocG1s4BRWxKxQwioT9o62NVDZ7+Xhbk3Zg5YOA5FXr1zB1yq3Oc1hobg/GU+fUztPBJzDxDNqljbTNz/U5NrZwmmkzKY9doWAUCfvq3VqGxaa9Lgj5YNUS1tkPJ5xZ2mVsfoaVZk8g7u+qrJjBJzsri7eiC8jb/QaEerdjYgunY7PSVFaMQsFoEnY9dW5TnQuW/xu8zTxjPqfbaoN5DguhiKTOpQmKyooZfLLtZl6MHI055Iatb/Y61q1H7EVZNhWxKxSMEmFv9QbZ0eghzWykoX4v8uO/wKRT+cA/uVthj+2QrGrxAaot3lCQY7fwaXQG7ZZ8+PKZXsfGrJixmTb8oeg+13JXKEYao0LY1+xpBbQuSd/nBQi2Ez3p5q7NlXViu09jzSFsStgHHbPRgMNq4cvsU2Db2+DteRdqzIoZk6XtbFVlBRSjnVEh7Kt2OzEaBJdOlVxqfJs9ZV/HmT6RcFR2b8Xou0+rnJqwq4h9aMhxWPjEfiJEQ/DVCz2Oc/lDGETHJy2VGaMY7YwKYV+9x8n0sZlM23gXEYy8mnsFjfrO0oJuWrXFIvZqPWK3m1VWzFCQYzezITIeCqbBuqd7HOfyhciwmcmwaX8nlcuuGO2MeGEPR6KsrWrlzPwGjBtf4MW0r7Oi2UqDK7nXaSI5dgsGkWjFjPi36aAkx2HB6Q3BYZdB9Rew/d1ux7n9YTLTTPG0VFW6VzHaGfGKtaXejTcY4Rz3k2DNZMP4y9i010Wj3sS6oJvGD0aDIDcmKqg89qEix27B6Q3CgishpwLeuhEiXaNxlz9EhtWMQ7fMVGaMYrSTMmEXQhiFEGuEEK+l6pqpYPVuJxNELcW1S2Hh96goKabBHWBznQvouUZ4Yqcfle44NOTYLTg9QTBZ4bQ/QONmfWNZMi6fHrFbtQewWjxVjHZSGbFfB2xK4fVSwuo9rfyv7XVNHBb9gGljMwH4aGsTDosRh7X7aDy2gGoxGTAaxKDNV9FBjt2MJxghEI7AlDNhwvHI9/9Aa1Nd0jiXP0SmLSFiV1aMYpSTEmEXQowDzgIeSMX1UknVrq2cKT9CHHYZpBcwbWwGoFk0vTV+iEXsKiNm6MjROy+1ekNa9c3T/oQMuHn9bz9Oqvro8oXITDOriF2h0ElVxH4XcAMQ7WmAEOJqIcRKIcTKxsbGFN22dxrdAc5sfx6DAI68FoC8dGs8xbG3Vm0xYVc2zNAR67zk9GpNTyiazhd5i7mQt2nYvjo+zuUPq4hdoUhgwMIuhPga0CClXNXbOCnlfVLK+VLK+QUFBQO9bb/YsmsXFxnfp3nCYsguix+P2TG9CXvMilF1YoaOHIcZgBZPMH7sUdsltJNG+kc3g5REopL2QHJWjIrYFaOdVETsRwHnCCEqgaeAE4UQj6XgugMm68uHsBEketR1Scdjwt7d5qQYyooZemIRe6u3oyzvFpeZu8Pnk1f3CWxbSrteiz3DZsZiMmA2Cjxqg5JilDNgYZdS/lJKOU5KWQ5cBLwnpfz2gGc2UALtTKp8gqXReeSUHZp0Kuaz9xaxFygrZsiJCXssYpdSUu308mjkFJqtpfD2r3B5tL0GmfrmJLvFhFdtUFKMckZuHvvqh7GFXTxu+joWU/LLnDVOa6xRmtNzq7YOK0blsA8V2XbNimnVPfZmTxB/KEoIE8/kXg1NWzGuWQJAZpo21mExqohdMepJqbBLKT+QUn4tldfcL8JB+PReNttm05A1q8vpinwHr117NGfMHNPjJToWT0fus+9gx2Y2YrcYafFoVky1U6u2aTYKXg/MhYpjKVj5V8bSTKZNF3arSXnsilHPyFSt9c+Au5anrN/o0W6ZWZLVpXNSIrl6qp3adTq05Ngt8Yi9Wi/KNqc0m6pWH5x5B0TDPGy5jWxDOwB2q0llxShGPSNP2KNR+OQuGHMob/mmU9hNka/+YDMbybF3FJZSDA05DjMtcWHXIvZFFXm0ekO4MyawbP7dlIs6KpZ+D0I+HBajitgVo56RJ+zrnoDmbUSP+gmN7cFui3z1l/sum8/3jzskhZNT7CtavZiYFeMl225mqr74XdPqY0f6PH4a+iG22uXw/FU4zAYVsStGPSNL2Pd+Cf/9GYw/Guf4MwhHJUW9ZL70xYLyXEqy01I4QcW+Eq8Xgxaxj8tJiy96V7X4cPlCvBY9gugpt8Lm1zg89LmK2BWjnpEj7N4WePrbkJYD33yIBo/2P3dvZQMUBz9alc0EYc+2My4nTf/Zq1d2NGE4/IeQOY7j2l5SWTGKUc/IEPZoBF74Hrhq4YJHIL2Qer0RdW+bkBQHP9l2M25/mFAkSrXTy7icNHIdFtLMRqqdPr2yoxmMJph/BRPbVzEmUDnU01YohpThL+wtu+CJC2D7O3DG/4PSBQA06PXW93fxVHFwEMtO2tHYjj8UZVxOGkIISnPTqGrx4vaHOha4D/sOYWHmG/ItoqqhtWIUM3xTPsIB+PQe+OgOMJjgjNth/nfjp2ONNAayeKoYerL13afrq9sAGKf76+Ny7FQ7fWSmmeI57KQXsKvwZM6r+wC/pxV7Rs6QzFmhGGqGZ8S+4308dy+C936PnHwa/GgFLPq+VtpVp8HlJ9NmwqZKAgxrcmPCXqMJe2luTNjTqHJ64002Ymyv+BYZwkdkbc89UhWKkc7wEva2GnjmO/Doufj8QS4P3kD1yf+CzOIuQxvcAbVwOgKIlRWICXuJvnBammPH7Q9T7fR2ROyAr2Au66PlWNc8CFLZMYrRyfAS9ndvga1vwgm/4uqMe/kgOocN+v/wnal3+dXC6Qgg5rFvrHWRYzeTrjfTiGXGuPzheJ0YALvVzCORU7G0bIGtbw3+hBWKg4DhJewn3ww//JzoMT9nU6OWAvdVravboQ3ugBL2EUCswmMgHI3760DS95kJu4MdViMvR47ClzURXv85BNoHb7IKxUHC8BL2zLGQW0G104cvpOUqf1XbNWKXUtLgDlCkrJhhT5rFiFWvzhmL0gFKczu+T4rYLSaCmNm84FZo2wPv/2HwJqtQHCQML2HX2VrvBrQqjd1F7C5fmGA42mu9dcXwIWbHJAp7VlqHLZPRKWIH2Js1V8uSWv4vqOm1uZdCMeIYnsLeoAn7uXNKaHAHaHD7k87HflaLpyODWMpjov0ihIgLfeLiqUOvxukJhDXrLr0IXvkxRDq6MCkUI51hKezb6tsZm2Vj0YRcoKvPXu+KbU5SEftIIFfvfZoYsWs/a0KfbMVoEbs3GAFbFpz5Z6jfAB//ZZBmq1AMPcNS2LfWu5lUlMH0Yq136cZOwh6P2JWwjwhiEXsshz1GtxG7bs94YoXApp0Nh14AH94OVSsGYbYKxdAz7IQ9EpVsb2hncmE6mTYz4/PsXRZQ4+UElBUzIohtUupcaTMu7AkblKwmA0aDwJtYuvesO7S9Di98T2XJKEYFw66kwJ4WL4FwlMlFWk3uGcWZXayYBlcAh8UYX1xTDG9OmlZIKBKNR+MxFs8pIRCOUpab7L3bLcaOiB3wG9Oxff3fsOQsePMXsPjeQZu7QjEUDLuIPZYRM6koHYAZxVnsbtbKt8ZocPtVtD6COH5KIbed37V3bUGGlWtOmIhIKCUB2gJqLGKvdnqZdfPbvNxaDkf/BNY8ChteGIxpKxRDxrAT9m1xYdci9u589gZXQKU6jmLs1o6I/bMdzQQjUW5/cwuBY26AcQvh5Wu0piwJ7GhsTwoOFIrhzLAT9q317ZRkp8VtlpnFWUByZkyD2682J41iHBaTlhUDrN7TitEgqGn18eTKOrjwMa0Zy1PfgvZGAKJRyXn/+JTb39zcr+vXtPr4ydNr+dmz6/o9p93NHq5+ZKXq7qQYFAYs7EKIUiHE+0KITUKIr4QQ16ViYj2xtd7NZN2GAe3jeGGGNWkBVZUTGN3YLUYtjx1YvdvJ0RPzWVSRy73vb8djyYOLHgdPEzxzKYSDVDt9tPlCLNve3Ot1fcEIdy7dykl/+YAX19Tw3Kpqvqxu7decPt7WxNsb69lWrxZvFQeeVETsYeB6KeU04HDgGiHE9BRct+uNIlF2NnriC6cxZhRnxq2Y9kAYbzCihH0U47BqEbvLH2Jrg5vDynK44fSpNLUHeWjZLiieC+f+HfZ8Bg9/jeptawDY1eShweXv8bo/f24dd7+7jVOmj+Gt/z0Wh8XIkmWV/ZpTLFOr2RMY8OtTKPpiwMIupdwrpVytf+8GNgElA71ud+xu8RKMROP+eoyZJVlsa2jn9fV7O1riqQYbo5ZYVsy6qlakhHnjc5g3PoeTpxXy74920uoNwszz4bwHoGkri95azI+ML2IizOe7Wrq9ZiQq+XBLIxfMH8ffLp7LlDEZfGPeOF79srbLzufuaNTHNLUHU/paFYruSKnHLoQoB+YCy7s5d7UQYqUQYmVjY+N+XT+2cJpoxQBctLCMyUUZ/PDx1Vz9yEpAtcQbzcSyYlbtdiIEzC7V1mGuP3UKbn+Y51fXaANnfROu+YJ16UfzM/OzPGf9PRu3bOn2mpvrXLgDYQ6fkBc/9p0jywlFJE8s39PnnBr03dDNStgVg0DKhF0IkQ48D/yvlLJLZS4p5X1SyvlSyvkFBQX7dY+tuj85sTBZ2Euy03j1R0fxu3NmxD/yjs1Swj5aiWXFrN7TypSiDDL0nanTxmZSkp3G6j3OjsHphdxo/Cn/zP8V0wx7+N6mK2BPl7iEFXokv6A8N35sQkE6x08p4LHP9xAMR3udU+y/yxZlxSgGgZQIuxDCjCbqj0spD1iScCgSZfrYTOyWrhuPTEYD3zmynPeuP56HLl/AhIL0bq6gGA04LCY8gTBr9jiZW5bc93RuWTZr93QseMbWbVoPOZsX5y3BHbEgl5wFy+5JKhy2otLJ2Cxbl3o1lx9ZTlN7gNfX7+11TjG7JhUR+zVPrOaIP73L8X9+n9Pv+oi/v78dqbpFKRJIRVaMAP4DbJJS/nXgU+qZ60+dwuvXHdPrmIIMKydMLTyQ01Ac5NitRqIS3P4w88Z3FvYcalp98bWYymZt3WZKUQaTDj2cc4K30lB0DCz9NfzzKNjxPlJKvqhsYUF5bpfNUMdOKmBCgYMln1b2OJ9IVMa99SbPwIQ9EpW8taGOHLuFWeOyybCZ+PNbW7j3ve0Duu5IJhKVXPvkGr7oYf0kFdS1+Xn0s8oDdv19JRUR+1HApcCJQoi1+r8zU3BdhWK/cCR8ojusLDvp3Fz95zW6HbM1vm6TwaxxWYTMWfyj6Ba4+GmIBOHRc/E/cBYneN/kqHFdPykaDIJTp49hQ00b0Wj3UXOLJ0hEP9fcPjArZm+bj3BUcukR47nn4rk8ffURnHdYCX9ZupX/fLJrQNceqWxrcPPqulqeXlF1wO7x3Koqfv3yVzQN8O+bKgZcTEVK+Qkg+hyoUAwSsdK9OXYzFfmOpHMzijOxGA2s2dPK6TPHsqXOjUFo6zZmo4H55Tksr3TCuafDISfA8n8RXvYAt5uXId9fAg1fh1Nu0bp56RRmWAlHJW2+EDl6U5BEYjZMhs00YCtmT4sX0Jp5g/Zguf38WfiCEW59bSPZaWbOnzduQPcYaayr0qy3z3f2vk9hIOxt0/7Grd4Q+elDn5E37HaeKhR9ESsWNrcsp4t1YjUZmVGSyRrdZ99a72Z8ngObWXsYLKrIZXOdG6cnCCYrHHUdt5Q/ysXiNlhwFWx8Ge5dAJ//EyLaJqh8fc9ET9FabOF02thMWjzBAfnh1S0+ILk1oMlo4O6L5jKjOJMHl6movTNrq7TNizWtPqr0B2OqiVl7rd6DI+tJCbtixBGL2Dv76zEOK8vhy5pWQpFol53Mi/R0xi8qO/zYFbudOMoXIM64Da75HMoWaVUiHzoDfK3kp2tReqO7e2Fv1FMdp4/NJBiJ4g7sf1mBKqcXg4DiTiWMLSYD88fnsKfZqxZSO7GuqpViPUtueSeffXezJyViXOfqiNgPBpSwK0YcZbl2TAbBMZPyuz0/tywbfyjKuqpWKpu9STuZZ43Lwmoy8NKaGiJRSYPbT2Wzl4UV+kMidwJc8py2ual2DTx2HkVmTbgbe4jYY9HclDHafRLtmDZviG8/sJw9zf2LJKtavIzNSsNs7Pq/blmeA3cgjPMgEZeDAV8wwpZ6N+fOLSHHbk6yY/yhCIv/vow73u5+78K+UNem/e1bfT2/9w1uP398fRPbGw58WQkl7IoRx4SCdDb87jRmjcvu9nwsBfL51dVEojJJ2K0mI98/dgJvbKjj+4+u5IMt2ma6xPx1hNA2N134KOz9kvFvXEoG3h53lTa4A2SlmeNRduIC6poqJ59sb2Lppvp+vbY9Ld4kGyaR8Xpd+spmT7+uNRr4qraNSFQytyyHhRW5ScL+xoa9tHpD1Lb2vXO4N0KRaLxURG/R/5Y6N/d9tHNQFliVsCtGJDHPvDuKs2wUZVp5ZW0t0BFJx/jpqVO4dfEM3tvcwC9fWE+a2cjMkqyuF5pyBlzwMMb6dSyx3I7T1WVfHqD3B8iwkqcvrCY+AKqdmmfeuQtYT1Q5fUmNRRIpz9eOd47+m9oDbKlz9+v6I421+sLp7HFZHD4hj2qnj2qn9v489YWWJTPQTKUGd4CY+9WbFbOrSXvgdl7QPxAoYVeMOoQQzC3NwROMYDYKyvO6/o926RHlPHj5AtLMRhZNyO3W+gBg6lmI8x9gnmErx2z9f9CNv93gDlCYaY1nS7Qk5LJX6SLzVU33D4VEfMEIje5APCOmM+Ny7AgBuzsJ++1vbuaSB7ruph0NrKtuozjLRmGmjUUV2vrJ8p0t7GxsZ/muFkwGMeD6PXVtHRG/s5eIfWejB7vFOCgFCpWwK0YlsXz2inwHFlP3/xscP6WQD35+PHddOKf3i834Ok+lXcii1v/Cqoe6nG5wBSjMsJGrR+yJEWIsy2VbgxtfMNLldxOJRZqdm3rHsJmNjM20sbuTFbO+xkVTeyDpgTJaWFfVyuxS7W89dUwGWWmaz/7MymqMBsHXZo2l2RMY0IJzbA1FiN499spmDxX5ji6ZWgcCJeyKUclhesZM5xLQnclPt5Jt75qb3pm3Cq5gpXkevH5DUq0ZKSWNen8Ai8mg5bJ7Eq0YLyaDICq1QmO9UdWHsAOU5dnZnZDSF4pE2d6g2TC7mkZXLfgWT5A9Ld64sBsMgkUVuXy6o5nnVlVz4tRCpo3NxB+Kxhuz7A+xiL08z0FbH1bMYNgwoIRdMUo5tCSLTJuJw8q6T4ncV/Iy7PyS6yBrHDzxTXj3Vmiroc0XIhiJxls15qdbkxbPqpw+jpyoZe90bsremapuctg7Mz7XkRSx72z0EIrI+PejiXXVMX+9YxF90YQ8alp9NLUHuGhBKXm6PTaQjWP1Lj8Wk4HyPHuPVkwwHKWqxTtowj7gnacKxXDEZjby8Q0n4rD2vMi6LxRkWKn0mpHffxax9Dfw8V/gkzsxFx/Bg+Z2Zq63Q3UO8y2nU90+GQBPIEyLJ8iiilzWVbX2uYBa1eLFZjZQ0MvOxvH5dprag7QHwqRbTWza2/Gw2Nk0yoS9qhUh4NBxHQvfh0/QspuKMq0cN7mAj7c3AdDkCVCW1/Mnod6oc/kpyrSS47DEK9B2Zk+Ll6gcnIVTUMKuGMVk2c0pu1Z+upVQRNJmH0/2xU+CsxJWPojcuJR84SNNGqBqObd53+RJ6zchfBjVTi1yL821M7Mkkw19LKDuafFSmmNP9mjDQTCaNYMXLWIHLTNmenEmm+pcWIwGxmTZ2DXaIvaqViYVpsf7IwNMG5NJRb6DC+aXYjIayHcMPGKva/MzJtNGdpqFth489spBzIgBJewKRUpI3H2abbdATjmccgtv513NT59Zx3sXHEeGI8iX9/8P33Y+Bf9eiz1rPlcZJTNdbraMmcL9nzkJRaI9ZuBUOX0c46iCJV+Dhk0QcEMkAHmT4OifwKwLGK9HnbubPUwvzmTzXjcTC9MpzrbF0+1GA1JK1lW3cVKnSq8Gg+C964+L/5yX3nVBe1+pd/mZWZJFtt1MeyBMMBztsiA/mKmOoIRdoUgJMXuksT2Q1LoxViemMNMG1nTen3Yr//hwJveZ36Ow8iVuMrfDu49zrTUPycnsqDqUqeVdi3hJTzPfbbmL88W74CiAaWeDLRPMDtj0Krz8Q/jgTxxy3K+B9PgC6uY6F0dNzCc/3cpH25qIRCVGw8iv2Vft9NHiCTKrtOsmtcRPPPFMpf3MGJJSUufyc/K0InL0T4BtvlB8TSXGziYPOXZzvxbiU4ESdoUiBXQUAksWiAZXAIfFGLcDch0Wlkbm0fKt/+MfH+zg1eWbWH55LtEP7+aGwNOEHnsNpn8NJp8GE06A2tXw5bOw6VW+jo+vSr/FoZf8CWwJG6aOuwG2LYUP/kTaK1fzo7TL2d1cRosnSL0rwLQxmaTbTATDUWpbfb1m1Qw1LZ4gu5ramTc+t+/BvRBbrzi0u41lCdjMRjKspv3eDeryhfGHoozJspGli3arN9hF2CsHMSMGVFaMQpESYhF7U6dCYA1uvxat68SzMDxBqlq8ZOXkIw45AdvlL3J+9DY2ZB6rifRz34XbK+Cx82HLGzgrvsZZwT9Se/hvkkUdNH998qnw3Tdh2jn8TC5h7q772bxXE7epYzPionKwL6DeuXQr5//zM257Y3OP9e37w8ZaFwYBU/pIZwXNjtlfjz1W/Kso0xaP2LvLZddSHQevq5uK2BWKFJCVZtZ3MXYW9kBS9Nbh6QapcvrirfYMBoGheDa/l7N5/keLoHol7PoICqfCpFP5bGMLW75c3eOuU0ArM/yNh/ji7m9xgethNnwYxsRpTBubSVTfgLOrsZ3jJu9fz+H9obLJQ7rN1O8a5Rv3urCaDPzrwx3samrnzgvndNsKsy++qnVxSEE6aZa+s57y0q3xWi/7SkzYx2TZsJm0e3UuK+AJhKlz+anIH7xPSipiVyhSgMEgyEu3dBH22OakGPnxiD1AtdObZIvMKM5i014XEQxaaeDjfq556SZrwuaknnPYATCaWDbzFh4Mn87Mqsd52XYL+YFqCtKtpFtNg7qA2uYNsfjvy7j5la/6NV5KydZ6N9+cP47fnj2dpRvrufi+z/tsFN4dG/e6mFGc2a+xeY7eI/anV+zhT29s6vZcvb45aUymjWw9Yu+cyx4ryjaYEbsSdoUiReSnW7vUZG9w+SnMSLBi9MW6nY0e3P5wUgQ+ozgTbzDSrfjuafGSYzeTYes7RXN8fjq3hC/jp/yU8YZ6+PexiPXPMqHAMahWzL8+2kGbLxTfKNQXdS4/bn+YKUUZXHFUBXdeOId11W08vXLfWtq1eILsbfMzPSbs/jb47B+w8iGoWQ2h5GqOeenWXuvFvL6+jvs+2hkvHdB5zgCFmda4sHfefVrZpD2UK/LsULkMovv+oNpXlLArFCkiv5NAtAfCeIIRCjM7IvZsuwUhOqoOxqwYIF5BckNN141KVS3efi96xlIeX/DP58GZj8KYWfDC1ZxtXdPj7tNgOMryFLaOq3f5eWjZLtLMRqpafD3mdycS29wTyyo6Z3YxC8tzuefdbXiD/W9OEls4nVlkg0/vhbtnw1u/hNf+F+4/Af5UAk9fCnUbAO1h2+IJ9Ojpt3qDSAmvrqvtcq7O5SfXYcFq0hbITQZBqy/5IbGrqZ1pYjdT3rkMlpwJm17p92vZX5SwKxQpoiAjuVxAQyyaS7BijAZBrt0S78OZKNaTCtOxmQ1x0U+k2tn/bJbxCdUqS8ZPgm8/D8VzuXzv78l2bcIf6loX5fnV1Vx43+f9bvjRF3e/u41IVHLjWdMAbTGzL7bWdTQWBy0t8YbTp9DoDrDk08p+33tjrYtZYgeLXj8d3v4VFB8GV38IP14LFzwCi/4Hdn4A/zoKnrmMckM9UdlzAa9Y45KX1tZ0OVff5qdIXxwX0QjZdnNyo5PGrSxcdxP/td6Ice9aOO1PMOXMfr+W/UUJu0KRIvLTrTS3d/Q0jeewJ1gxoGdh6HnTiVaMyWhg1rhs1nQSdn8oQrXTG2+k0Rd5DgsOfdFw6tgMsNjh4icJW7N5wHwH1Xt2dPmd2KeEnSkoFLazsZ2nV1TxrYVlnD5jDNC/evNb690UZFjjueUA88tzOWlqIf/6YEevBbYSsW96lmett2AEuPQluPQFKJ4DuRUwfTGc9ge4bh0cewNsf4+zVn+PQpw9blJyeoI4LEY21Li6dD+qc/k5yroDHjoLfl/AkuhNHFH9IHz5DDx8Dvx9AXPb3uF1x3lw3Vo44odgOvC57CkRdiHE6UKILUKI7UKIX6TimgrFcCM/3UIwEsXl02yDjs1JyRkhefo29gyricy05IyPuWXZbKxtS4qq1+xpJRSRzC/vX8EyIQTj8xwYDYKJhfqCXcYYas54iEw8FLx6OfiTI+jNerS8p5dmz1JKnvpiD54eerb6ghE+3d7ETS9twGoy8KMTJ1GQYaUww9q/iL1T/9kYPzttCu5AmH9+2PWBlETID2/8gkvr/sRO2wy4+gM45ITux9pz4cRfwRWvYwm5echyOy3Oli7DQnqP2nPnlmAQ8HIsao9GofITbnDezE1110HTVljwPWyGCGc3PwgvfA+ad8CJN3G6+CefTvwJpKWm4Fx/GHC6oxDCCPwdOAWoBlYIIV6RUm4c6LUViuFELK2xsd1Plt3Mtno3BgFjs7pG7ADjcu1danPPLc0hFNnJV7WueDPuz3c2YxTLjvkAABTrSURBVBBa9NpfZpZkYjMbsJo60v3GTlnItaFreaD1TnjiQs2isdiRUsY7LPVmxWza6+YXL6zHYBBcML80flxKyfcfXcX7WxoIRSQGAb86a3r8/ZhRnNln5cpoVLK1vp2LFpZ2OTdtbCaLZxfz0LJdXHPCIV0XkKXUfOu3b4LWPTwUPp22w37LNEden+8TY2ex99R/MuW/l9Py/jUw6SUwdshiLHVxypgMjpmQza5VS5HRhxFfvQjuWuZKO8vKf8hRl9wEFge3Na7A01LHk+cXQsk8nP4oO15fykXdNHM5kKQiYl8IbJdS7pRSBoGngMUpuK5CMayIlxVwazbLW1/VsbAit4sQxVIeS3O6pi7GGoCs2eOMH/t8ZzMzirPI7EdGTIxbFs/k0SsXJR1zWE18lX4Ej5fcBHs+g6cvgXCAaqePdj0K391LxF7bqpUNrtHb+cVo9YZ4e2M9x00u4KHLF7D2t6dy5dEV8fMzirPY3tjerbcfo6bVhy8U6bE+/tmziwmEo8kt/qSEHe/Dw2fDM5eBJYOtpz/B78KXMa2k/w9B2/TT+XX4CgrrP4ZnvwPtDR2vzePnHMOnnLr2xzxQ9w3uDfwK+cV9UDyH5tP/weGBe6ma8QOwaMKdlWZhT8ChpasaTexqHtwaMTFSsUGpBEjMR6oGFnUeJIS4GrgaoKysLAW3VSgOLjrKCgTY0djO1vp2bj57epdxMQ95XDebjYoybZRkp8V9dn8owpqqVr5zxPh9mktPPV8r8h28GFrEpYvvhZevgWcuY/v0W7X5p1up6kXY9+qLwTGBj1Gj//yNeaWc0KnoFmgReySqfSqY3U3tFiAu2JML06FlF1R+AruXaRaHKY0jhZV7zF7sHy6FxpmaFbLyQWjcBPZ8OOsvcNjlfLGiBtjQ7xx2gBy7haeiJ3FaeTrHb/sn3DsfTrkVMsZQ8sZvuMeyGb+nFDnrQq5ZmUPJoady4/lHULm7BS+fUZTwiUxbPO3IitmuZ/r8//bOPTiu+rrjn7MrrbTaXWklS7Iea/khP2Rj+QHGQNIUGxhqHo2TAIYAwdMQ0mRIQyYhDZRpMqWT6ZDQNDMlTesJj7QlaSDk4fBIcHlDivEDMAbLOH5gy15ZsqXVw3pLv/5x713v6mFprZXWuzqfGc/uvXt17+9nXX3v2XPO75zq0qnLYYfkCPtIFYWG5Q0ZYzYBmwBWrVp19muFFeUcxbHET3T08PvdDQD8xdKyYcc5rpjRFhutqAryzmFL2N8+HKG3f5CL543DrTAO5pX4eWZXGLPiFqS/B579JqsPbuMvXZ/FV7OBzbvCGGNGbN/W0GoJeLg1Pp/bEfbQCN9AwLLYwVoNOpqwf9jYTgUnWP7K7XDwRWtn3gwoq4WBPnJ7TrLCFabi0HY4aAdRy2ph/b/B0usgOzd6jQJvNpXBMRZyxeBkKj1fcANrrrnVSov83VetD32z+GrvV/jiTXezNFSInNrJozsbkLw9zLOt8LKYkhGFedl09g7Q0z9ATpabD8Jt5Hnc4w58J4tkCHs9EOsYCwHDEz4VJcMJerNx22UFXtt3ghWzgpQXDBcYJ3g6WnmAlbOCPLMrTGNb91n518/E8lABP9t6mL3H26m58HYIXciJx77Av3oeor7hHZ7rvY2mjp5hmTxwWtCHWey2a6ZiFDGdVeQlkJs1embM4CDFe/6bLbk/JqveDZd/BxZdBSU10TrzAvzNQ6/j97h4/Ka5Vsni4gXRzx0+CLexpDw/4b6iVr2YHiiphY1Pw/u/gv4enu65mM2/qeNbfuv/4/71S8nNdvMfrxyIXjpW2J1CYK1dfZQG3OwJt7GoLIBriitqJkPYtwELRGQucBS4Cbg5CedVlLTC5RJm+Dy8e6SVXfWt3HNVzYjHXTS3iM+srGT1vJHFeqXdru/tI5Gof73Am5ymIJcutFwlL9U1UVOWD+XL+EL2P/F5/wvc2LyJJzyHaDiylNIl5w37Wae359FIV5xVfzTShTfbbRXBatwDe56GpjpoOwptR5FABfcGFvPHw6vBLD0txsbAvufhlQfYcHwHu3PPZ+lfPwaFI7udFs4M8NLeJsgvB8oBaOvu48E/7KWsIJfF5fnUhdv43MWJua3AethGywq4XFB7PQAnX7YycZwCX0U+Dw/esJzbLpnNPz79gV1///TvJloIrLOPEn8OdQ3tXF1bnvB4JsqEhd0Y0y8iXwH+ALiBR4wx4ysOoSgZRkkgh9ftdmtODvdQCn0efnDjilHPcV5FPtlu4c0DJ3n7SITbzkKoRsMRwJf3NvLlNdV09w2w/2Q34bUbCZdcSsVvNuL+3WegZDOULIr7WUfYe/oHaT7VG61U2dx8gm96NyM/+jac2AsIBKus/q+h1XByHze3P8rNPIr53n1I6WLr3Ed3QvgdTLCKewa+REHtRpaOIupgCfuTO+ppPtUbjVP8fncD//l/H8Udt3SMUr0jMcPvGTFzJ9LZiyfLhXdIzGJZKMiTX/rYsOODXqd0bx/h1m5au/pYUj52hclkk5TqjsaYZ4Fnk3EuRUlnHD97TVmAOWeZCZGb7WZJRQG/3F6fVP+6w5pFJWx69QBt3X0cPmn14qwpz6d48RV85sm/54n+B+HhK+ETX4cL/gpy8zHGWPVXCvvZ3zJIuLWbGV437HyM7xy8n6BpBf8nYPUdVuGyQPxD7ZnXd/D6c4/zrcVdBDv2w+6nrIYh63/EgfJr+MUP/8iDZWcOeC6wc9w/PN4e/T/ZdrCZwrxsXr57LXUNbRyNdHFV7cgP1DMxtMm4Q0tnL0V5nnG7dmILgXX0WLGAmvLxB3KThZbtVZQk4gj7uhGCpomwclYw2oz5wrnJ8a87rF1Uyo9f3s8b+05E0xwXlQXIyXLTEqjhh6GHuG/w32HLt+HVf4ZlG+hra+AF1xtUdDVDLvQ96gdPDnSeZD9LeHP+97nz1htHveb8+Qu5c+ByVi9czqdXhiw3jC2W+3aHrTGMUTt9UZn1+b4YYX/rUDOr5hRRkJfNRRN4AM7weWjv7o8GPR1aOvviXC1jEVsIrMl+UNSUTb3FriUFFCWJFAesr+ITFnY7n/28ivyk+dcdzq8KEsjN4qW9jdQ1tJOT5WKOvYCmakYeb3cUwsbfwR0vQvUa2P4wHHuXbYM1bF/4db7Xt4EPKz4JC66k9/r/4rru+zAV55/xmtUlPnKyXLzvNOyOsYD3NnQgwulVsqNQlp9LICcrWizseFs3H53s5KIkPPiibqUhLfJaTvVSmEA7O6f1XaSrlw/CbXbgOLm/v/GgFruiJJHrzg+Rn5s9rs49Z+J8O4B60dzkumHAqknz5wtKeHlvEwtm+llUFoj2Qa0qyrMClACVF1hFswb6eWNfM3c9to2nPn4JP/lgK/1lczjv6sXUN3UAr4yaERN7zZqyALtHyIypa2ijqihvzKYYIsKCmX72Hrdy3t86aJUAuDAJGUOxDVBiM5laOnuj3xTGg8/jJtsttHT2URduswLUKUAtdkVJIgtnBrhz7fyE0+2GMqsojweuq+WOT8xL0sjiuXRRCY3tPWw90Bz3EJo9w0dTe098mVx3VjTVsSLopTLojeauO6/jyRuvDRXw/tG2YeVxd9W3jtmb1GFRWYB9x9sxxrDtUDN5HndCi5FGo9gW9qF+9khnX0INqEWEAq+H463dHDxxisUp8K+DCruinLPceGEVZQXD88mTwRq7PV7/oIkL7lXZC2mONMfnqje0duESq2xCeUHusPIClaMsToplWShIe09/dJk9wMmOHo5GulgWGp+wLygN0NLZx4mOXt462MwFswvJck9cxpy1BbGdlIwxRLr6KEpA2MHys2892MygISUZMaDCrijTktL83KiluzjG1eAI+0cn4xtyhFutTlBZbhcVQW9U2I9FLMGfmT/2A8gR710xHZXes8sFLwuNvCJ1KE4tmW2Hmtl7vJ3VSVq4FXXFxPQ+bevuZ2DQJBQ8BSuX3fkmo64YRVGmlMtrSnG7JM5id7ovDS3f29DWHf32UBH00tjeQ9/AIPWRLsryc8keh9U8v8SPN9vNu0dO+9l31bciwrjdKQvLrADrz986jDHJyxjy52ThyXLFWewRu+ZLIsFTsAqBAeR53NEH5VSjwVNFmaZ8ec181taUxjW2KPBmE8jNGibs4dZuFthZK5XBXIyxFiwdi3SNGTh1yHK7OK8iP2qlgyXs84p9484cKfFbvUVf23cCj9vFilFqzySKiFDs88S1NnQyZAp9iVvsQEpKCTioxa4o0xSvxx0tX+BgNenIixN2YwzhSFfUYneyRo5Fujga6RqXf91hWSjI+8da6R+wGjq/dzTC8nG6YZzxLSwN2OcqGLWK5dlQkp9LuPV0bMGpxZ5I8NQ63hL2VAVOQYVdUZQhVBXlxTXcaLebcpfHuGLA6sPa0No9bosdLDHu7htkX2MHx9u6Od7WQ+04A6cOjjtmdZIXblUX++KafTvldxMPnlrHq7ArinLOUFXk40hLJwN2WqJTI6bMttQrgpbAv1tvtexLpERubAB1V31r3L7x4gRQk70it7rUT0Nbd3Q1rtOUOlEfe9RiT8GKUwf1sSuKEsfsGXn0DRjCrV2ECvOiOeyOxZ7nySKYl822Q1aXp0SEfc4MH4GcLHbVt1Lk8+B2CUvKExP2q2vLOdrSxceqk7t4q7rE+iZwoKmDZaEgkc5eXAKB3MRkcs2iUm67ZPa4M30mA7XYFUWJw8lQecOuUuk02Ijt3VpR4KWuwSoPkIiP3eUSakMF7Kq3ShsvKPWPueJ0KMX+HO69enFcTZdkML/UKquwv8kqWdB8qpdgnifhAGhl0Mv965fiyUqdvKqwK4oSR21lAfNL/TyxvR6wMmJEiGu+URH0Yszp94mwLBSkrqGNd+sjCbthJpOqIh9ul7C/0fKzRxIsAHYuocKuKEocIsKGVSF2fNTC/qYOGlq7KfbnxFmglbafvcCbjT8nMVfFslABfQOGSGdfSt0VQ/FkuZhdlBe12Fs6EysAdi6hwq4oyjA+tbISt0t4cns94dbuODcMQHnQCaQmZq1DfLD0XLLYweoJe1rY+1TYFUXJHEoDuaxdVMpTO+s50tIZ19cTTgt6IoFTh8qglyKfh2y3JFQ5cSqoLvVx6EQn/QODRDp7o4uN0g0VdkVRRmTDqhBN7T0caDo1zGJ3XDHOayKICJfMm8EFswuTHgCdKNUlfnoHBqlv6bJcMb70tNg13VFRlBFZW1NKsd9aZl9WEG+ZhwqtGiizzrIWyoM3LGfQmLEPnGKclMfdx1rp7hvU4KmiKJlFttvFp1dWAgyz2Gfm57Lpcxew4cJZZ3Vur8eNL8Gg61RQXWKlPG63c/TVx64oSsZxy0WzqS7xjVhs68rzyshPQdu3ySSY56HY72HHR+kt7OfeI1NRlHOGOcU+XvjGmlQPY0qZV+KPEfb0fHBNyGIXke+LSJ2I7BKRX4vIuZOUqiiKchZUl/ijdXLSNXg6UVfMFmCpMWYZ8CFw78SHpCiKkjocPzswPYOnxpjnjTFO19s3gdDEh6QoipI6qu2GIgBB7/S02GP5PPDcaB+KyBdFZLuIbG9qakriZRVFUZLHfDvlMWC3y0tHxgyeisj/AmUjfHSfMea39jH3Af3A46OdxxizCdgEsGrVqnMvgVVRFAVrVW1Olotggi3xziXGFHZjzBVn+lxENgLXApcbcw6uOFAURUkAt0uYW+xLW2sdJpjuKCLrgG8BlxpjOsc6XlEUJR342hULSWc7daJ57A8BOcAWEQF40xjzpQmPSlEUJYWsWzqS9zl9mJCwG2PmJ2sgiqIoSnJIXyeSoiiKMiIq7IqiKBmGCruiKEqGocKuKIqSYaiwK4qiZBgq7IqiKBmGCruiKEqGIalYXSUiTcBHZ/njxcCJJA4nHdA5Tw90ztODicx5tjGmZKyDUiLsE0FEthtjVqV6HFOJznl6oHOeHkzFnNUVoyiKkmGosCuKomQY6Sjsm1I9gBSgc54e6JynB5M+57TzsSuKoihnJh0tdkVRFOUMqLAriqJkGGkl7CKyTkT2isifROSeVI9nMhCRR0SkUUR2x+wrEpEtIrLPfi1M5RiTiYjMEpGXRGSPiLwvInfZ+zN5zrki8paIvGvP+R/s/XNFZKs951+IiCfVY002IuIWkbdF5Gl7O6PnLCKHROQ9EXlHRLbb+yb93k4bYRcRN/Aj4CpgCfBZEVmS2lFNCo8B64bsuwd4wRizAHjB3s4U+oFvGGMWAxcDd9q/10yecw9wmTFmObACWCciFwMPAP9iz7kFuD2FY5ws7gL2xGxPhzmvNcasiMldn/R7O22EHVgN/MkYc8AY0wv8D7A+xWNKOsaYV4HmIbvXAz+13/8U+NSUDmoSMcaEjTE77fftWH/0lWT2nI0xpsPezLb/GeAy4Jf2/oyaM4CIhIBrgJ/Y20KGz3kUJv3eTidhrwSOxGzX2/umAzONMWGwhBAoTfF4JgURmQOsBLaS4XO2XRLvAI3AFmA/EDHG9NuHZOL9/UPgb4FBe3sGmT9nAzwvIjtE5Iv2vkm/tyfazHoqkRH2aa5mhiAifuAp4GvGmDa7OXrGYowZAFaISBD4NbB4pMOmdlSTh4hcCzQaY3aIyBpn9wiHZsycbT5ujDkmIqXAFhGpm4qLppPFXg/MitkOAcdSNJap5riIlAPYr40pHk9SEZFsLFF/3BjzK3t3Rs/ZwRgTAV7Gii8ERcQxtjLt/v448EkROYTlRr0My4LP5DljjDlmvzZiPcBXMwX3djoJ+zZggR1F9wA3AZtTPKapYjOw0X6/EfhtCseSVGw/68PAHmPMD2I+yuQ5l9iWOiLiBa7Aii28BFxvH5ZRczbG3GuMCRlj5mD97b5ojLmFDJ6ziPhEJOC8B64EdjMF93ZarTwVkauxnvJu4BFjzHdTPKSkIyI/B9ZglfY8DnwH+A3wBFAFHAZuMMYMDbCmJSLyZ8BrwHuc9r3+HZafPVPnvAwraObGMq6eMMbcLyLzsKzZIuBt4FZjTE/qRjo52K6Yu40x12bynO25/drezAJ+Zoz5rojMYJLv7bQSdkVRFGVs0skVoyiKoowDFXZFUZQMQ4VdURQlw1BhVxRFyTBU2BVFUTIMFXZFUZQMQ4VdURQlw/h/2GwEIddShrYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoothing = 0.9\n",
    "z_val = infer_z(smoothing)\n",
    "\n",
    "plot(x, y);\n",
    "plot(x, z_val);\n",
    "title(\"Smoothing={}\".format(smoothing));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Smoothing \"to the limits\"\n",
    "\n",
    "By increading the smoothing parameter, we can gradually make the inferred values of the hidden Brownian motion approach the average value of the data. This is because as we increase the smoothing parameter, we allow less and less of the variance to be allocated to the Brownian motion, so eventually it aproaches the process which almost doesn't change over the domain of $x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/repos/pymc3/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "/repos/pymc3/pymc3/tuning/starting.py:102: UserWarning: In future versions, set the optimization algorithm with a string. For example, use `method=\"L-BFGS-B\"` instead of `fmin=sp.optimize.fmin_l_bfgs_b\"`.\n",
      "  warnings.warn('In future versions, set the optimization algorithm with a string. '\n",
      "logp = -6.6522e+06:   1%|          | 52/5000 [00:00<00:04, 1058.44it/s]\n",
      "logp = -1.3071e+07:   2%|▏         | 108/5000 [00:00<00:05, 835.78it/s] \n",
      "logp = -3.0073e+07:   5%|▍         | 238/5000 [00:00<00:06, 737.98it/s] \n",
      "logp = -4.3473e+07:  10%|█         | 520/5000 [00:00<00:05, 845.90it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = subplots(2, 2)\n",
    "\n",
    "for ax, smoothing in zip(axes.ravel(), [0.95, 0.99, 0.999, 0.9999]):\n",
    "\n",
    "    z_val = infer_z(smoothing)\n",
    "\n",
    "    ax.plot(x, y)\n",
    "    ax.plot(x, z_val)\n",
    "    ax.set_title('Smoothing={:05.4f}'.format(smoothing))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "This example originally contributed by: Andrey Kuzmenko, http://github.com/akuz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
